I have tried asking chatgpt, i have tried searching animations, I just dont get it!
Edit: I finally get it. If you choose a wrong door, then the other wrong door gets opened and if you switch you win, that can happen twice, so 2/3 of the time.
In: 296
I’ll walk you through, hopefully it helps.
First off – when you’re looking at probability, we often frame it as “The chance that I’m right,” but it’s actually more helpful to think of probabilistic events in the context of, “What’s the most likely thing to happen?”
For example, take rolling a six-sided dice. What are the odds of you rolling a 6 within six rolls? Well, an intuitive (but wrong) answer would be to say, “well, there’s a 1 in 6 chance, and I have six rolls, so I think they’re pretty good! 100%!” And that’s wrong.
If you look at it that way, you’re computing the wrong probability. You need to rephrase the question: It’s not whether you *will* roll a six. It’s, how likely is it that you *won’t* roll a six? So if you do that math – yes, you probably will roll a six at some point in those six rolls, but there’s a pretty good chance that you won’t. There’s a 33% chance that you could roll that die six times and not get a six.
So, how does that relate to the Monty Hall problem? Well, you’re looking at it as if the doors are independent of each other. There was a 33% chance that you guessed correctly the first time, and now that there’s two doors, you have a 50% chance to have it right now. But if you think about it that way – you’re thinking about it incorrectly.
It’s not about whether you guessed right the first time: It’s whether you guessed *wrong* the first time. Do it that way, and it should become clearer. What are the odds that you guessed incorrectly on your first guess? Well, two doors are wrong, one is right. So you had a 67% chance of being wrong.
Once you come to the second pass – the car and the goat can’t switch places. So the odds are that there’s a goat behind the door you already picked. Then the host removed the OTHER door that had the goat. Meaning, the only door that’s left has the car behind it.
If the car and the goat could switch places, then your intuition that it’s a 50:50 chance would be correct. But since they can’t, once the host removes one of the goats, the only way for you to lose is that the door you initially picked had the car behind it. There’s only a 33% chance of that happening, so if you always switch doors after the host reveals the goat you have a 67% chance of winning the car.
You’ll still lose sometimes, of course, but that’s the strategy that will get you a car more often.
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